高数求救 (以下2为平方)求下列方程所确定的隐函数y的二阶导数d2y/dx2：arc tany/x=ln√x2+y2，详细过程哦

Question

如题所述

Answer 1

追问

我等号后面是ln，你给的是log,为什么答案会一样...

追答

我打错了.. 应该是ln 哈哈

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Answer 2

(xy'-y)/x^2(1+y^2/x^2)=(x+yy')/(x^2+y^2)
xy'-y=x+yy'
y'=(x+y)/(x-y)
y''=[(x-y)(1+y')-(x+y)(1-y')]/(x-y)^2
=[x-y+(x-y)y'-x-y+(x+y)y']/(x-y)^2
=[-2y+2xy']/(x-y)^2
=[-2y+2x(x+y)/(x-y)]/(x-y)^2
=-2y/(x-y)^2+2x(x+y)/(x-y)^3本回答被网友采纳